How to completely fill an object with fluid?
There is no shortcut at all. My idea could be select the inner side of your container mesh and duplicate it with Shift + D. 
Then press P to separate the selection into another object.
You can try to make new mesh closed by selecting its top loop and pressing F and with luck get it close without much work (the mesh must be closed the Fluid sim to work).
Then add Fluid modifier in Physics panel.